Question

Work out the equation of the line which has a gradient of ½ and passes through the point (4,2).​

Answer 1

the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

`(\stackrel{x_1}{4}~,~\stackrel{y_1}{2})\hspace{10em} \underset{gradient}{\stackrel{slope}{m}} ~=~ \cfrac{1}{2} \\\\\\ \begin{array}ll \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{ \cfrac{1}{2}}(x-\stackrel{x_1}{4}) \\\\\\ y - 2 = \cfrac{1}{2}x-2\implies y=\cfrac{1}{2}x`